Electricity from ambient heat

Discussion in 'Physics & Math' started by Frencheneesz, Oct 3, 2008.

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  1. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    Call the rock´s heat removed or used by the engine H and the energy used to drive the engine E.

    Then the heat added to the "cold room." is H+E. Thus slowly your cold room becomes hotter than than the out side air (assuming it is well insulated).

    What you have is an initially cold sink for an engine to reject part of solar energy to (and rest becomes work), but the operation of the engine destroys this cold sink, just as if it were a block of ice as each rock transfers H+E into the room or into block of ice.
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  3. Tom Booth Registered Member

    Ummm... An air conditioner is just like a block of ice ?

    Not unless you didn't install the air conditioner/heat pump properly.

    Usually in a window to vent the hot air removed to the outside more or less continually.

    Call the heat removed by the heat pump or air conditioner H3

    So what's that do to the equation ?

    H + E - 3H = ?

    Remember, we are talking about an open system. The room can have a window for the air conditioner. It doesn't vent the heat removed back into the room.

    Besides that. It is a Stirling Engine. It runs on the heat "removed from the rock by the engine" so H and E are the same thing. Right ? Or did you mean something else ?

    That is "the rock´s heat removed or used by the engine H" and "the energy used to drive the engine E." are the same quantity of energy. No ?

    So we have H - 3H.
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  5. Tom Booth Registered Member

    Lets add some details just to make this clear.

    The conveyor belt and the hot side of the heat engine are housed within a Dewar chamber (Thermos).

    The only way heat can enter the room is by passing through the engine and exiting the cold side of the heat Engine.

    Qc = Qh – W

    The heat engine is coupled to an electric generator that powers the air conditioner which has a COP of 300% (the air conditioner / heat pump removes 3x more heat than it consumes in electrical power)

    The AC consumes W energy. The work output of the heat engine.
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  7. Tom Booth Registered Member

    As a side note.

    Regarding the earlier discussion about the efficiency of a Stirling Engine running on heat (with Ambient as Sink) Vs a Stirling Engine running "on ice" Ambient as the heat source and a sink below ambient.

    This statement of Carnot from his work Reflexions sur La Puissance Motrice du Feu translated by Dr. Robert H. Thurston:

    Apparently a 1 degree temperature differential at cold temperatures can produce more power than a 10 degree temperature differential at much hotter temperatures.

    Why ?

    The density of the medium used for expansion and contraction ?

    Cold air is more dense and so packs more of a punch ?

    I don't really know. Just speculating myself here.

    Anyway, I would assume Carnot would be accepted here as an authoritative source on this subject. Not the one I was looking for or had read originally but perhaps this will do.
  8. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    The statement you quoted started: "a given quantity of heat will develop more motive power..."

    It is the heat not the temperature which can be converted partially into high quality energy, work when a colder "sink" is available to receive the "waste heat" - that part of the heat which cannot by any device be converted into work. I.e. there is a max efficiency, E, possible for this conversion of heat H into work, W given only by the hot source temperature, Th, and the cold sink temperature, Tc, which is: E = (Th -Tc)/Th.

    I.e. the best that is possible is W = [(Th -Tc)/Th] x H where all temperatures are on the Kelvin (or absolute) scale.

    As your quote did not tell which temperature scale was being used, it is impossible to tell if it is true or not. I will assume that the kelvin scale was used. Then, E = (1010-1000) / 1010 or a little less than 0.01 or a little less than 1% of heat H can be converted into work W.

    In the 1 degree and zero degree case, I will first assume that the centigrade scale is being used. (Its degrees are same size as K scale and 1C = 274K). then E = 1/274 which is a little less than 0.004 and less than the first case.

    If, however, the Kelvin scale is also used in the 1 & 0 degree case, then 100% of H can be, in principle, converted into work, W; but 0 degrees K has never been achieved and to even get close takes a lot of energy.

    I have in other threads noted that energy for moon base can be efficiently converted from sun light with two buried loops of coils. One is covered for 14 Earth days when sun is shinning on the surface and only exposed to the very cold sky radiation at night time. The insulating cover is on the hot coil at night and gets unfiltered sunlight light (>1KW / m^2) for 14 days. I.e. Tc > 500K and Tc < 50K may be possible, when lightly loaded (little work is being done). Then E = 450/500 = 0.9 is the limit which is nearly 4 times greater than the theoretical max efficiency of silicon solar cells*, and about 6 times better than best real PV cells. Thus, in practice, solar thermal conversion can be more than three times better than photo cells on the moon as a permanent energy source, ALL BECAUSE VERY LOW Tc IS POSSIBLE.

    *Until our sun becomes a red giant with spectral distribution better matched to silicon PV cells.
    Last edited by a moderator: Jul 7, 2012
  9. Tom Booth Registered Member

    I don't really know what you mean by "It is the heat not the temperature".

    The heat that can be converted into useful work is generally determined by the temperature difference.

    The reference reads:

    Heat isn't a THING exactly, but a process. A transfer of energy. But anyway.

    Bad assumption. I think we can rule out the Kelvin scale. Carnot was writing in 1824. The Kelvin scale wasn't invented until around 1848, more than ten years after Carnot died. No ?

    I don't mean to be obstinate but it doesn't make any sense to make comparisons based on different scales of measure. By that sort of comparison I could prove that an inch is much larger than a foot ; an inch being a full 2.54 centimeters and a foot being only a fraction, 1/3 of a yard.

    I could prove that water gets hotter when it freezes and ice gets cold when it melts. Ice measures 32 degrees and melted ice measures just 1 degree.

    Carnot's statement: “The fall of caloric produces more motive power at inferior than at superior temperatures.” is broadly stated and should hold true using any scale of measuree. You can't make any sense out of it however if you assume kelvin in the first part and centigrade for the second part of the very same sentence:

    Does it make any sense to slice that sentence up into two different temperature scales ?

    Or assume a scale of measure that wasn't invented yet ?

    It seems to me that Carnot was writing in terms of real engines. I think he probably, no doubt based his statement on actual observation or experiment. He wasn't talking about impossibilities or things that didn't exist or couldn't possibly happen. Like running a heat engine at absolute zero.

    Again, Carnot was speaking broadly and his statement was, I think, meant to apply to any scale at any range, or at least within the known ranges and real possible operating temperatures of actual heat engines in his own time. His statement was certainly not intended to be limited to the cryogenic range, the near absolute zero range, the kelvin or any other scale and certainly not to MOON BASE.

    Simply: "more motive power at inferior than at superior temperatures"

    Plain and simple. You get more power at colder temperature ranges for the same temperature difference.
  10. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    That is correct. Carnot was only 28 in 1824 when he wrote Réflexions sur la Puissance Motrice du Feu ("Reflections on the Motive Power of Fire"). A wide ranging discussion, which did include the engine cycle we now call the Carnot cycle. He probably did know it was the most efficient possible working between two fixed temperatures, but never gave a formula for calculating the the efficiency of the cycle because, as you noted, Kelvin* is credited with being first to realized there was a minimum possible temperate which he called zero degrees on the "absolute scale" that now is called the Kelvin scale.

    "... {Carnot} showed that the efficiency of this idealized engine is a function only of the two temperatures of the reservoirs between which it operates. He did not, however, give the exact form of the function, which was later shown to be (T1−T2)⁄T1, where T1 is the absolute temperature of the hotter reservoir. (Note: This equation probably came from Kelvin.) ..."
    From: http://en.wikipedia.org/wiki/Nicolas_Léonard_Sadi_Carnot

    Perhaps the statement you quoted as from Carnot was to use the Rankin scale or, more probably, he was just trying to indicated, as you also realize, that more energy can be converted from fixed amount of heat energy dropping a fixed temperate range when the temperature of the cold sink is lower. Without the yet to be invented kelvin scale, he could not prove his assertion, even if he had known the correct efficiency formula, which he did not.

    My mention of my suggested moon base energy system, was to drive home the fact that on the moon a cold sink temperature of ~50K may be possible and thus permit much more efficient conversion of thermal energy into work, smaller collectors etc. for same output. (At least 3 times more efficient than the usually suggested solar cells system.)

    Same thing I mean when I say: "Apples are not oranges." Heat and temperate are two very different things. One is measured in Joules and the other in degrees. (MKS system)

    You seem confused and treat temperature as if it is something that can be converted into energy - it can not be. No more than apples can be converted into orange juice.

    *BTW, Kelvin at one point was in charge of canon making factory. He noted that the workers poured water into the vertical castings as they were being bored (canon ball size) to keep the cutting tool from getting too hot. He realized that work was being converted into heat, which then was called phlogiston, which was then considered to be conserved but less concentrated in colder objects. I.e. when hot object was pressed against a cold object, the invisible mass less phlogiston flowed from the hot to the cold object until the concentrations were equal.) The phlogiston theory was very useful as all caloric changes are correctly modeled by it. Kelvin was first to realize that work could make new phlogiston and found how much. (4.186 units of work units, to make one unit of phlogiston if memory serves me correctly). This is an early example, of the very common advance of science on the backs of military needs.
    Last edited by a moderator: Jul 8, 2012
  11. Tom Booth Registered Member

    I would assume that what Carnot probably had in mind was Steam Engines.

    Practically speaking, it would probably be difficult if not impossible to have a cycle involving steam or water where the temperature would drop below freezing.

    Based on that, I figure he was probably thinking on the centigrade scale which was the primary temperature scale at that time.

    Again though, talking in regard to the principle, it shouldn't matter what scale is used so long as it is adhered to.

    I would be very interested to know if the math backs up Carnot's statement.

    You say: "more energy can be converted from fixed amount of heat energy dropping a fixed temperate range when the temperature of the cold sink is lower."

    For instance, take an ambient temperature of 50 degrees F (or the equivalent on whatever scale) and a 100 degree TD (temperature differential)

    How does it compare in terms of actual or theoretical efficiency if the TD is above or below ambient ?

    That is, either a hot side at 150 degrees F and a cold side at 50 F or

    a hot side at 50 F and a cold side at -50 F

    Or maybe I'm asking the wrong question. But does a heat engine, all else being equal, run more efficiently at lower temperatures as Carnot seems to be suggesting ? What do the numbers actually show ?

    -50 degree Fahrenheit = 227.5944444 kelvin
    50 degree Fahrenheit = 283.15 kelvin
    150 degree Fahrenheit = 338.7055556 kelvin

    According to http://www.onlineconversion.com/temperature.htm

    To make the calculations easier we could make the values 230, 280, 330 K which would be proximately the same as -50, 50, 150 F
  12. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    The Carnot efficiency, E is (Th-Tc) / Th
    E = 1- Tc/Th
    E =1 - Tc/(Tc+D) where D is the temperature difference (positive number)
    E = 1 - 1/[1 + (D/Tc)]

    To make E larger we need to make [1 + (D/Tc)] bigger. (If it were very big, E approaches unity.)
    To do that, we need to make Tc smaller as both 1 and D are fixed.

    Last edited by a moderator: Jul 9, 2012
  13. Tom Booth Registered Member


    E is (Th-Tc) / Th
    E =(330-280)/330


    E is (Th-Tc) / Th

    E at 100 F above ambient 0.15 < 0.18 (E at 100 F below ambient)

    Is that right ?

    These results seem awful small (less than 0.2)

    What exactly do these numbers represent ?

    If the efficiency at a 100 degree F Temperature Differential is less than 0.2 how could an LTD Stirling Engine possibly run at all on a 1 degree temperature difference ? (As I've seen in some advertisements for these engines (claims of engines running on a 4 or 5 degree TD are more common) or the heat of your hand etc.


    For (280-279)/280 for example = 0.004

    BTW, to answer the earlier question, could a Stirling Engine run on evaporative cooling (like the drinking bird)

    Here is a video of a guy running an LTD engine with nothing more than a wet piece of paper on top. He apparently measures a temperature difference of 4.4 C

  14. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member


    Yes those 15% & 18% efficiency LIMITS are correct if your temperatures were in degrees K. (and again shows the greater value of a colder sink - which could be only 50K in the moon energy system I have suggested years ago in posts, or that least 3 times more efficient than solar cells most suggest).

    You can get some work from even smaller than 50K difference, but that is the difference the "working fluid" experiences. In most cases there is a pair of heat exchangers coupling the working fluid to the enviromental sink and source with 5 or so degrees across it unless it is very big and expensive but when the energy is with zero cost as in OTEC, working between (273+30)K surface water and (273+5) cold bottom water (a 25degree TD) and reduced to say 15degee TD in the working fluid due to the temperature drops across two heat exchangers, the E = 15/(273+25) and quite low, with most of the thermal energy just passing thru the heat exchangers to warm bottom water.

    That nutrient rich water then stays near surface to greatly increase biological use of sunlight and ultimately produces more fish to catch.

    The first major study of OTEC was lead by Dr. Avery of APL/JHU >35 years ago where I worked. It showed OTEC was economical, even back then when oil was was cheaper. I have been an OTEC supporter for three decades as an fish eater, and one concerned with the lack of protein many suffer from. Main reason, I think, why no large OTEC exists is the unknown insurance cost. How often will storm break the long vertical pipe, if X dollars were spent on it, etc. I think governments should offer affordable insurance to the first dozen of so OTECs that are built until private industry knows what to charge for insurance. OTEC´s potential energy is more than 10 times larger than all the wave energy systems could ever collect.
    Last edited by a moderator: Jul 9, 2012
  15. Tom Booth Registered Member

    I think I'm having a bit of difficulty with the rationale behind these efficiency ratings.

    Let's take ambient against absolute zero as the TD.

    Using the same ambient temperature as previously we get:

    E is (Th-Tc) / Th

    So 1 represents 100% efficiency ?

    Then 0.18 would represent 18% efficiency correct ? (Move the decimal point 2 places, or 0.18 x 100 No ?

    OK, what I'm having a problem with is that these efficiency ratings seem to be based on the potential of Total energy. That is, the comparison is being made against absolute zero.

    This does not seem to be a refection of how much heat actually entering the engine is being converted. In other words "available energy" as reflected by the temperature differential vs "total energy" as reflected by whatever temperature against absolute zero.

    In other words, the way I read this is that even if 100% of the "heat" or kinetic energy passing into the engine were converted to electricity and NO heat reached the sink, the "efficiency" would still only be 18% in terms of "total energy" rather than "available energy", because if the cold side were absolute zero more of the "total heat" (measured against absolute zero) could be converted or in other words the other 82% of "unavailable" heat that would be made available on the way to absolute zero could have been converted.

    If I'm getting this right or interpreting this correctly, this does not seem to be a "fair" way of determining "efficiency".

    I would think that efficiency should be determined based on "available heat" or how much of the kinetic energy entering the engine is actually converted into some other form not based on how much could potentially have been converted with a "sink" at absolute zero.

    In other words, if an engine were designed so as to effect its own cooling

    i.e. Qc = Qh – W

    Where the work performed is used for refrigeration. even if 100% of the heat entering the engine were used to power the refrigerator (Qh = W) and No heat entered the sink so that the temperature of Qc would actually decrease, the so-called "efficiency" would still be determined to be around only 18% since there is still a long way to go before things bottom out at absolute zero.

    Am I interpreting the rational behind these efficiency calculations correctly ?

    If so then it would seem that "efficiency" has no real bearing on how much of the "available" heat or the heat (kinetic energy) actually entering the engine is converted to some other form or whether or not the energy extracted is used to effect additional cooling of the sink as we are measuring against a "what if" type criterion. That is, even if we convert all the heat entering the engine and use it for cooling the sink, (at 18% efficiency) we could still do better if the sink were even colder all the way down to absolute zero (100% efficiency), as the determination of efficiency is based on Total heat (against absolute zero) rather than available heat (the actual TD).

    Anyone care to take a stab at straightening out my thinking on this ?

    In my mind I would say that if 100% of the heat actually entering the engine is being converted then the engine would be "100% efficient" at converting energy regardless of the temperature difference, but this appears not to be the case. Instead "efficiency" is being measured against the hypothetical potential for additional heat conversion with a "sink" at an unrealizable absolute zero.

    In other words, no matter what until we hit a wall at absolute zero we can still do better even if we are already converting 100% of the "available" heat.
  16. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    To TB:

    If 0 degree K cold sink were available and did not warm as heat is added, then thermal energy at any Th >0 could in principle be 100% converted into work; however, coldest natural point in the universe is ~4 degrees K.

    Mankind, with great use of energy has made small collections of atoms colder than that but only by doing everything possible to prevent any heat entering the cooling mass.

    Even a perfect (no friction) Carnot engine can not produce enough work to drive a real refrigerator to pump the heat the engine deposited in the cold sink back up to the hot source, even if 100% of the work produced by the engine is used to drive the refrigerator.

    Give up your silly idea that you can both get work for other uses and still return the heat dumped in the cold sink back to the hot source. (close the cycle) It is a violation of conservation of energy.

    TB said: "this does not seem to be a "fair" way of determining "efficiency"...." You can hold that POV, but Nature does not give a sh-t about your POV. Physical facts in the natural laws are facts, and not up to popular vote as to the "fairness."
    Last edited by a moderator: Jul 9, 2012
  17. Tom Booth Registered Member

    Well, I can agree it is a "physical fact".

    Just by comparison,

    Suppose we have a platform that absorbs an impact from a dropped ball, and we drop the ball from six feet to the ground. Does it matter if we are on top of a mountain and drop the ball six feet or if we are at sea level and drop the ball six feet ?

    However if we dig a hole so the ball can be dropped a greater distance we could absorb and convert more energy at the platform.

    If the platform absorbs and converts ALL the energy developed by the fall should we not consider that our platform is "100% efficient" rather than comparing it with a hypothetical hole that reaches all the way to the center of the earth (the equivalent of our absolute zero) and so determine that it is only .000001 efficient (or some such infinitesimal number) ?

    Our cold sink Tc is our "ground". A physical limitation. Sure. The ball cannot be dropped any further than the bottom of the hole, but so what ? This doesn't really say anything about the platforms ability to absorb and convert the energy developed in the fall it just makes a comparison against a hypothetical hole that we might dig, if it were possible, all the way to "China".

    And why, if our platform is only 18% "efficient" by such a reckoning, can we not, nevertheless, use the energy thus converted to drive a digging machine and so make our hole progressively deeper with each impact ? If only by a hairs breadth.

    Looking at the "Free Piston Lamina Flow" Stirling driving a linear generator.

    It is a glass test tube. Glass conducts little heat. Most of the heat from the flame applied is no doubt just going around the test tube. Comparatively little heat is getting through the glass and into the engine.

    Taking this small amount of heat that is actually getting to the inside of the engine, if the engine were not converting nearly 100% of that heat into electricity the piston would not be drawn back. There is no flywheel to push it back. If all the heat were not going somewhere, being converted, the engine would stall, which it can be demonstrated to do if the load is removed. Without a load there is no conversion of energy, or very little so the result is that heat build up immediately and the engine cannot operate.

    I would conclude that such an engine, along with the LTD engine running on a piece of wet paper, that either engine is converting nearly 100% of the available energy, though the Carnot efficiency rating would apparently give these engines an infinitesimally small efficiency rating simply due to the "physical constraint" or the shallow depth of the "hole" which doesn't happen to reach to the theoretical maximum, all the way to the center of the earth.

    Given such a method of reckoning efficiency, I can see no real reason why any heat engine with a 1% "efficiency" rating could not maintain or even deepen its "cold hole" as Carnot efficiency apparently has nothing to do with the heat actually entering the engine or the amount of heat converted or even the amount of heat actually reaching the sink, but rather is making a comparison against how much more heat could be converted if the "hole" were as deep as it could possibly ever be.

    So why can't the energy absorbed and converted by our "platform" at the bottom of the hole be used to dig the hole a little deeper ?

    In particular, if we are using ambient heat and the "balls" dropped are converted, we neither run out of energy nor do we have to toss the balls back out of the hole to use them over again.

    It is not a case of returning "the heat dumped in the cold sink back to the hot source."

    When heat is associated with physical matter it can be moved along with the physical element it is attached to. Otherwise a Heat Pump could not remove more heat than it consumes in whatever other form of energy. The heat is attached to the air being blown through the heat pump by a fan. A heat pump is sometimes or usually I think, looked at as a "closed system" but in reality, it has matter passing through it, air being blown through "the system". If it were a "closed system" it would be violating the 2nd law of thermodynamics.

    IMO, to say that heat is converted into work or electricity but still needs to be sent back to the hot source AS HEAT is itself a violation of conservation of energy.

    Energy cannot be created or destroyed. It can only change form. So if you make heat into electricity (Change its form) it is no longer heat and if you could make electricity out of heat and still have the heat to return to the hot source then your energy would be doubled. You could have "perpetual motion", you could create electricity from heat and still have the heat to use over again.

    Once converted the heat is GONE. The heat/energy has changed form and become electrical energy or "motive power" or whatever it was converted into. If you still had the heat after making that energy into electricity, THAT would be a violation of the law of conservation of energy.
  18. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

    to TB:

    I will not bother to correct your invented physics more. You refuse to learn when I do. Perhaps you will read at least a high school level physic book and then stop posting your nonsense - your false versions of how nature should be in your opinion.
  19. Pete It's not rocket surgery Registered Senior Member

    Because the hole is made deeper by pulling stuff out, but energy is extracted by dropping things in.

    At 100% efficiency, you can get enough energy to pull out everything you dropped in, so the hole is just as deep as before.
  20. Tom Booth Registered Member

    So, in other words, you arn't going to attempt to refute this:

    When you convert heat into some other form of energy, the result is a drop in temperature. The "heat" has diminished, changed, been converted, and some other form of energy is the result. You can't still have the heat and the new form of energy it has been converted into as well. The heat is gone. The consequence is a drop in temperature.

    Anybody could supply textbook references galore to support this. Simply put, you know you cannot refute it.
  21. prometheus viva voce! Registered Senior Member

    Mentioning perpetual motion is the finger of death for this thread. Since we are quite clearly going nowhere it is closed.
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